Nonlinear photogalvanic effects in two-dimensional materials, particularly the nonlinear circular photocurrents (NCPs) that belong to the helicity-dependent spin photocurrents, have sparked enormous research interest. Although notable progress has been witnessed, the underling origin of NCPs remains elusive. Here, we present systematic photocurrent characteristics, symmetry analysis and theoretical calculations to uncover the physical origin of NCPs in MoS_{2}, a prototypical 2D semiconductor. Our results show that the NCP responses in 2D semiconductor MoS_{2} result from the circular photon drag effect (CPDE), rather than the generally believed circular photogalvanic effect. Furthermore, we demonstrate that the NCPs are highly tunable with electrostatic doping and increase progressively with MoS_{2} thickness, evidencing the interlayer constructive nature of CPDE responses. Our Letter unravels the critical role of the previously overlooked CPDE contribution to NCPs, revolutionizing previous understanding and thus providing deep insights into further fundamental studies and technological advances in nonlinear photovoltaic and opto-spintronic devices.